Problem: What is $(3+3+5)\div2 - 1\div2$ in simplest terms?
Solution: Note that the term inside the parenthesis must be simplified first, \[(3+3+5) = 11.\]This is substituted back into the original expression,  \[11 \div 2 - 1 \div 2 .\]Since $a\div c - b \div c = (a-b)\div c$, we have \[ 11 \div 2 - 1 \div 2 = (11-1) \div 2 = 10 \div 2 = \boxed{5} .\]